I have sent a lot of thing from Spain to USA. I think the Swedish post will be similar.

It's easy, the seller only have to go to the post office with the bumper packed and pay the shipping costs. Usually from Europe to USA it will take two weeks to arrive.

If the pack are too big is possible (depend of swedish post normative) that they don't want to send it. In this case you will need to use a private carrier agency but it's always more expensive (but more fast).